There is known a vehicle provided with an engine, a supercharger to raise the pressure of intake air introduced in the engine, and an automatic transmission constituting a portion of a power transmitting path between the engine and drive wheels. Patent Document 1 discloses a control device for a vehicular drive system used for this type of vehicle. In the vehicular drive system disclosed in Patent Document 1, the automatic transmission is a continuously variable transmission the speed ratio of which is continuously variable. The control device of Patent Document 1 is configured to control shifting actions of the automatic transmission such that a rate of change of the speed ratio (shifting speed) of the automatic transmission in an initial stage of a shifting action is made higher when a rate of change of an operation amount of an accelerator pedal, namely, a rate of increase of the accelerator pedal operation amount is higher than a predetermined value, than when the rate of increase is not higher than the predetermined value. This manner of control of the shifting actions permits a rapid rise of the intake air by the supercharger upon an operation of the accelerator pedal by the vehicle operator to accelerate the vehicle, thereby improving a response of the vehicle to the vehicle operator's operation to accelerate the vehicle.